To me, this man is not marriage material, as it stands right now. I think if I were in your position I would be looking for someone else to take a primary role in my life. This man could make a nice secondary if he was willing, but I would be thinking of marrying someone else, that is, if he doesn't do some major work with you.
Normally, I don't subscribe to primary/secondary, but time quantities and investment. I wouldn't be investing too much or looking for quantities of time with him, as he doesn't get poly, doesn't seem to want to, and isn't interested in looking at his jealousy or the pain he feels to find a positive way in it. We all feel jealousy at some points, at least most of us do, but looking at it and working through it makes one stronger and more apt at dealing with it. He doesn't sound interested or wants to avoid his feelings.
It's just not possible for the long haul, or for a married relationship, not to look at one's shit, poly or not. Stuff comes up and if it isn't dealt with in a timely fashion, then it ends relationships. You have the advantage of *knowing* a huge bit of shit before getting married; that is a gift. He is not accepting this gift of knowledge. To me, that's a tell-tale sign, if he is unwilling to work on it. Other issues will be no different. He likely won't want to deal with other shit, either.
Life is hard work, marriage is hard work, poly is hard work, work is hard work. We all need to get on it and push fear aside. The larger issue, to me, seems to be that he is not dealing with his fear. If I were you, I would be addressing it as such, and if he still doesn't deal, then I'd move on.
What are you asking him permission for? Does he own you? Is he the one that rules over you? I don't think so. You do. I understand that you want to be respectful, but you are creating disrespect from him about your nature. I think you should stand firm and tell him who you are dating AND let him know you love him. Stay firm with what you need, do what you say you will do, give him the same kind of information each time and stick with your expression of love.
You cheated. He doesn't trust you. And why should he? Stay confident and consistent and that will change in time, I think, or it will be evident that it just won't work between you and him. All this is said with much love and care.
DADT is a cop-out, a way of avoiding real issues a lot of the time, imo. It's an *open* way of doing things, but I haven't known it to work for the long haul in terms of deepening and strengthening relationships. Relationships naturally want to become deeper and more connected. It's part of human nature to do so, or they end.
He seems to be good at avoiding or not dealing with your polyness, so challenge him on it, or you will never, in my opinion, have a deeper or more connected relationship. And really, isn't that what you would want for a marriage?
Make him face stuff and see what he's made of. The time is now, no? After all, you plan to marry him. If he is the man for you, would he not rise to the occasion and give your relationship everything he's got, rather than avoid?